Simple analytical method for calculating the field integral of general permanent multipole magnets

Permanent multipole magnets are now used in various fields, especially in accelerators or ion sources. The magnetic field integral is important for designing such magnets in view of beam optics. A simple method for calculating the magnetic field integral of permanent multipole magnets is described. The analytical treatment is based on the reciprocal theorem of mutual inductance, which converts the original three-dimensional calculation into two-dimensional one. This calculus exactly considers the effects of the end field and tapered magnet pieces as well as the use of an iron magnetic shield sheath. The results are summarized in simple forms, and are useful for designing permanent multipole magnets.